The Congressional Budget Office might have inadvertently boosted a Republican effort to strengthen the border security provisions in the Senate immigration package.

The nonpartisan CBO, in its review of the "Gang of Eight" comprehensive reform legislation, predicted that the bill would reduce illegal immigration by just 25 percent compared to current law. Sen. Bob Corker, R-Tenn., who with Sen. John Hoeven, R-N.D., is negotiating a bipartisan amendment to beef up the existing proposal's border security measures, said CBO findings could be just what Republicans need to convince Democrats that tougher enforcement measures are needed.

"The 25 percent CBO number, that laid out that this was only going to make the border 25 percent more effective, certainly has gotten [the Democrats'] attention, and a lot of people on our side's attention," Corker told reporters Wednesday afternoon. "The CBO report said, that while this scored heavily, the border was only going to be 25 percent more secure with the bill as it was. So, that's been incredibly helpful to us last night and this morning."

Corker and Hoeven were headed into another round of talks on their amendment, which is intended to secure additional Republican support for the "Gang of Eight" bill, without losing Democrats. Some in the chamber are referring to it as "Cornyn-lite," after an amendment by Senate Minority Whip John Cornyn, R-Texas, that would significantly strengthen the border security triggers in the Senate bill; Democrats rejected that proposal as too Draconian.

Corker said the negotiations have gone back and forth, occasionally appearing to bear some fruit, before heading in the opposite direction. Hoeven said he remains "hopeful," but doesn't expect to know if Democrats and Republicans will be able to agree on the measure until Thursday. "Until we have an agreement," he said, "we do not have an agreement."

The CBO score of the "Gang of Eight" package showed that the legislation would reduce federal deficits by nearly $1 trillion during its first 20 years, and proponents of comprehensive immigration reform touted those positive numbers. But critics of the bill weren't swayed, and found plenty in the CBO report to use against the proposal.

One such finding involved whether enactment of the gang's bill would reduce illegal immigration, and by how much.

Here is what the CBO score said on that subject: "CBO estimates that, under the bill, the net annual flow of unauthorized residents would decrease by about 25 percent relative to what would occur under current law, resulting in a reduction in the U.S. population."